Mass transfer and metabolic reactions in hepatocyte spheroids cultured in rotating wall gas-permeable membrane system

Isolated hepatocytes in spheroid configuration exhibit a high degree of cell–cell contacts, which are important in the maintenance of viability and liver specific functions. In the absence of a vascular network, the cells in a large spheroid size experience mass transfer limitations of metabolites and oxygen in the core of aggregates. In this paper transport phenomena related to the diffusion and reaction of oxygen, glucose and lactate are mathematically described and experimentally verified for hepatocyte spheroids cultured in a rotating-wall polystyrene system (RWPS) not permeable for gases and in a rotating-wall membrane system (RWMS) with oxygen-permeable membrane. The concentration profiles of glucose, oxygen and lactate in the hepatocyte spheroids were estimated for different diameters of aggregates by solving the mass transfer equations for simultaneous diffusion and reaction, by finite element method. Simulation results evidenced that, for aggregates with size lower than 300 μm cultured in both RWPS and RWMS systems, the concentration profiles of glucose and lactate towards the core of spheroids (effective diffusion coefficients in the order of 10−11 m2/s) are not significantly affected by the metabolic rate (c.a 10−6 μg/mm3/s for glucose and about one order of magnitude less for lactate). On the contrary, the transport of oxygen (diffusion coefficient: 3.4×10−10 m2/s, reaction rate: 1.5×10−5 μg/mm3/s) is critically affected by the size of the multicellular spheroids and significant gradients in oxygen concentration may develop in spheroids. Aggregates with a size greater than 200 μm suffer severe oxygen limitation in the most part of its size attaining the lowest partial pressure in the centre. The improved viability predicted by the model culturing hepatocyte spheroids in the RWMS, characterized by a higher O2 permeability with respect to RWPS, was experimentally confirmed. The results demonstrated that the mathematical model used in this study represents a useful support to experimental procedures in order to obtain hepatocyte spheroids with optimal size.